
If this transformation is a symmetry of the action then, under the assumption of invariance of the path-integral measure, the correlators satisfy the following identity [1]}:
\(\langle \mathcal {T}{\Phi _1}(\mathbf {x_1^\prime }){\Phi _2}(\mathbf {x_2^\prime })\ldots {\Phi _n}(\mathbf {x_n^\prime })\rangle =\langle \mathcal {T}{\mathcal {F}}({\Phi _1}(\mathbf {x_1})){\mathcal {F}}({\Phi _2}(\mathbf {x_2}))\ldots {\mathcal {F}}({\Phi _n}(\mathbf {x_n}))\rangle \) 
